A duality method for mean-field limits with singular interactions

Abstract

We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. In case of first-order systems, it allows to recover in particular the mean-field limit to the 2d Euler and Navier-Stokes equations. The approach also provides convergence rates.